Closedness Type Regularity Conditions in Convex Optimization and Beyond
نویسندگان
چکیده
منابع مشابه
Closedness Type Regularity Conditions in Convex Optimization and Beyond
The closedness type regularity conditions have proven during the last decade to be viable alternatives to their more restrictive interiority type counterparts, in both convex optimization and different areas where it was successfully applied. In this review article we deand reconstruct some closedness type regularity conditions formulated by means of epigraphs and subdifferentials, respectively...
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In the paper, we describe various applications of the closedness and duality theorems of [7] and [8]. First, the strong separability of a polyhedron and a linear image of a convex set is characterized. Then, it is shown how stability conditions (known from the generalized Fenchel-Rockafellar duality theory) can be reformulated as closedness conditions. Finally, we present a generalized Lagrange...
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In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions. The first regularity condition we give guarantees the surjectivity of the monotone operator S(· + p) + T (·), where p ∈ X and S and T are maximal monotone operators on the reflexive Banach space X . The...
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We give some new regularity conditions for Fenchel duality in separated locally convex vector spaces, written in terms of the notion of quasi interior and quasi-relative interior, respectively. We provide also an example of a convex optimization problem for which the classical generalized interior-point conditions given so far in the literature cannot be applied, while the one given by us is ap...
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ژورنال
عنوان ژورنال: Frontiers in Applied Mathematics and Statistics
سال: 2016
ISSN: 2297-4687
DOI: 10.3389/fams.2016.00014